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Once I posted in the following thread and wondered, how I could picture/understand conservative forces best. I think, that I understood my problem now and everything became clearer. So just for confirmation, correct me if I am wrong:

You have two electrons A and B at positions P1 and P2 and you move A to a point P3. Moving P1 to any point on the circle around P2 with the radius | P3-P2 | you have to do the same work.

This seems quite obvious to me right now. However I think my problem was, that I always tried to include the mass of electrons in my thoughts, which amount of energy to you have to put into the system to make the electron move.. (is it even possible for electrons to stand completely still? whatever) well, my problem was that I imagined that you always have to apply a force, whenever the direction of the movement of the electron on the path changed. Well, that is still true, however now I understand it this way, that you don't do any work, if you move around equipotential field lines. I find this a bit weird though, even if you have to use in an infinitely small force. However the overall picture looks right. Ah, just remembered the centripetal force and now it might become clearer.

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Imago
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You appear to understand the situation quite well.

For a conservative force, the amount of work done going from A to B is independent of the path taken.

A slightly more formal definition is that the curl of the force field is zero. This results in any closed path having zero net work done (by Stokes's theorem). As the route from A to B and back again by a different route can be considered a closed path and the line integral from B to A is minus the integral from A to B, this leads to the path independence of work done.

And yes, your comment about centripetal force makes sense - a centripetal force at right angles to the direction of motion will do no work.

ProfRob
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